Properties

Label 170.2.o.a.7.1
Level $170$
Weight $2$
Character 170.7
Analytic conductor $1.357$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [170,2,Mod(3,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([12, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.o (of order \(16\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 7.1
Character \(\chi\) \(=\) 170.7
Dual form 170.2.o.a.73.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.923880 + 0.382683i) q^{2} +(-0.518138 - 2.60485i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.404835 - 2.19912i) q^{5} +(1.47553 + 2.20829i) q^{6} +(-1.33574 + 0.892510i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-3.74516 + 1.55130i) q^{9} +O(q^{10})\) \(q+(-0.923880 + 0.382683i) q^{2} +(-0.518138 - 2.60485i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.404835 - 2.19912i) q^{5} +(1.47553 + 2.20829i) q^{6} +(-1.33574 + 0.892510i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-3.74516 + 1.55130i) q^{9} +(0.467546 + 2.18664i) q^{10} +(-3.02313 + 2.01999i) q^{11} +(-2.20829 - 1.47553i) q^{12} -3.47326i q^{13} +(0.892510 - 1.33574i) q^{14} +(-5.93814 + 0.0849082i) q^{15} -1.00000i q^{16} +(0.483478 - 4.09466i) q^{17} +(2.86642 - 2.86642i) q^{18} +(5.49423 + 2.27578i) q^{19} +(-1.26875 - 1.84127i) q^{20} +(3.01695 + 3.01695i) q^{21} +(2.01999 - 3.02313i) q^{22} +(-2.02929 - 0.403651i) q^{23} +(2.60485 + 0.518138i) q^{24} +(-4.67222 - 1.78056i) q^{25} +(1.32916 + 3.20887i) q^{26} +(1.55482 + 2.32695i) q^{27} +(-0.313408 + 1.57561i) q^{28} +(-0.814533 - 4.09494i) q^{29} +(5.45363 - 2.35087i) q^{30} +(4.50895 + 3.01279i) q^{31} +(0.382683 + 0.923880i) q^{32} +(6.82817 + 6.82817i) q^{33} +(1.12028 + 3.96799i) q^{34} +(1.42198 + 3.29876i) q^{35} +(-1.55130 + 3.74516i) q^{36} +(5.44865 - 1.08380i) q^{37} -5.94691 q^{38} +(-9.04734 + 1.79963i) q^{39} +(1.87679 + 1.21558i) q^{40} +(2.21131 - 11.1170i) q^{41} +(-3.94184 - 1.63276i) q^{42} +(4.83901 + 2.00438i) q^{43} +(-0.709326 + 3.56602i) q^{44} +(1.89531 + 8.86406i) q^{45} +(2.02929 - 0.403651i) q^{46} -1.43673 q^{47} +(-2.60485 + 0.518138i) q^{48} +(-1.69117 + 4.08284i) q^{49} +(4.99796 - 0.142959i) q^{50} +(-10.9165 + 0.862208i) q^{51} +(-2.45597 - 2.45597i) q^{52} +(3.14380 + 7.58981i) q^{53} +(-2.32695 - 1.55482i) q^{54} +(3.21832 + 7.46597i) q^{55} +(-0.313408 - 1.57561i) q^{56} +(3.08132 - 15.4908i) q^{57} +(2.31960 + 3.47152i) q^{58} +(-1.18771 - 2.86738i) q^{59} +(-4.13886 + 4.25894i) q^{60} +(14.2603 + 2.83655i) q^{61} +(-5.31867 - 1.05795i) q^{62} +(3.61800 - 5.41472i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(-7.63810 - 1.40610i) q^{65} +(-8.92144 - 3.69538i) q^{66} +(-0.280368 + 0.280368i) q^{67} +(-2.55349 - 3.23723i) q^{68} +5.49515i q^{69} +(-2.57612 - 2.50349i) q^{70} +(8.39457 - 12.5634i) q^{71} -4.05373i q^{72} +(-2.74845 - 1.83646i) q^{73} +(-4.61914 + 3.08641i) q^{74} +(-2.21724 + 13.0930i) q^{75} +(5.49423 - 2.27578i) q^{76} +(2.23524 - 5.39634i) q^{77} +(7.66996 - 5.12490i) q^{78} +(-8.99386 - 13.4603i) q^{79} +(-2.19912 - 0.404835i) q^{80} +(-3.34351 + 3.34351i) q^{81} +(2.21131 + 11.1170i) q^{82} +(5.82251 - 2.41176i) q^{83} +4.26662 q^{84} +(-8.80890 - 2.72089i) q^{85} -5.23770 q^{86} +(-10.2447 + 4.24348i) q^{87} +(-0.709326 - 3.56602i) q^{88} +(-3.47194 + 3.47194i) q^{89} +(-5.14317 - 7.46402i) q^{90} +(3.09992 + 4.63936i) q^{91} +(-1.72035 + 1.14950i) q^{92} +(5.51161 - 13.3062i) q^{93} +(1.32737 - 0.549814i) q^{94} +(7.22897 - 11.1611i) q^{95} +(2.20829 - 1.47553i) q^{96} +(-1.67183 - 1.11708i) q^{97} -4.41923i q^{98} +(8.18850 - 12.2550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{10} - 40 q^{15} + 16 q^{18} + 8 q^{20} - 8 q^{25} + 8 q^{26} - 72 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} - 64 q^{33} - 24 q^{34} + 32 q^{35} + 16 q^{37} + 32 q^{39} - 8 q^{40} + 16 q^{41} - 40 q^{42} + 48 q^{43} + 16 q^{44} + 24 q^{45} - 64 q^{47} + 16 q^{49} + 32 q^{50} + 32 q^{51} - 16 q^{52} - 24 q^{54} + 8 q^{55} + 8 q^{56} - 8 q^{57} - 16 q^{58} + 64 q^{59} - 48 q^{60} - 24 q^{61} - 24 q^{62} - 24 q^{63} - 16 q^{65} - 16 q^{67} - 16 q^{68} + 24 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} - 8 q^{75} + 40 q^{77} + 48 q^{78} - 72 q^{79} + 8 q^{80} + 48 q^{81} + 16 q^{82} + 16 q^{83} - 8 q^{85} - 64 q^{86} + 24 q^{87} + 16 q^{88} - 16 q^{89} + 48 q^{90} + 48 q^{91} + 8 q^{92} + 8 q^{93} - 8 q^{94} + 40 q^{95} + 16 q^{97} + 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.923880 + 0.382683i −0.653281 + 0.270598i
\(3\) −0.518138 2.60485i −0.299147 1.50391i −0.779257 0.626705i \(-0.784403\pi\)
0.480110 0.877209i \(-0.340597\pi\)
\(4\) 0.707107 0.707107i 0.353553 0.353553i
\(5\) 0.404835 2.19912i 0.181048 0.983474i
\(6\) 1.47553 + 2.20829i 0.602383 + 0.901530i
\(7\) −1.33574 + 0.892510i −0.504861 + 0.337337i −0.781778 0.623557i \(-0.785687\pi\)
0.276918 + 0.960894i \(0.410687\pi\)
\(8\) −0.382683 + 0.923880i −0.135299 + 0.326641i
\(9\) −3.74516 + 1.55130i −1.24839 + 0.517099i
\(10\) 0.467546 + 2.18664i 0.147851 + 0.691477i
\(11\) −3.02313 + 2.01999i −0.911507 + 0.609050i −0.920429 0.390911i \(-0.872160\pi\)
0.00892150 + 0.999960i \(0.497160\pi\)
\(12\) −2.20829 1.47553i −0.637478 0.425949i
\(13\) 3.47326i 0.963309i −0.876361 0.481654i \(-0.840036\pi\)
0.876361 0.481654i \(-0.159964\pi\)
\(14\) 0.892510 1.33574i 0.238533 0.356990i
\(15\) −5.93814 + 0.0849082i −1.53322 + 0.0219232i
\(16\) 1.00000i 0.250000i
\(17\) 0.483478 4.09466i 0.117261 0.993101i
\(18\) 2.86642 2.86642i 0.675622 0.675622i
\(19\) 5.49423 + 2.27578i 1.26046 + 0.522101i 0.910051 0.414495i \(-0.136042\pi\)
0.350411 + 0.936596i \(0.386042\pi\)
\(20\) −1.26875 1.84127i −0.283701 0.411721i
\(21\) 3.01695 + 3.01695i 0.658354 + 0.658354i
\(22\) 2.01999 3.02313i 0.430663 0.644533i
\(23\) −2.02929 0.403651i −0.423136 0.0841671i −0.0210709 0.999778i \(-0.506708\pi\)
−0.402065 + 0.915611i \(0.631708\pi\)
\(24\) 2.60485 + 0.518138i 0.531714 + 0.105764i
\(25\) −4.67222 1.78056i −0.934443 0.356112i
\(26\) 1.32916 + 3.20887i 0.260670 + 0.629312i
\(27\) 1.55482 + 2.32695i 0.299225 + 0.447822i
\(28\) −0.313408 + 1.57561i −0.0592285 + 0.297762i
\(29\) −0.814533 4.09494i −0.151255 0.760411i −0.979720 0.200370i \(-0.935786\pi\)
0.828465 0.560041i \(-0.189214\pi\)
\(30\) 5.45363 2.35087i 0.995692 0.429208i
\(31\) 4.50895 + 3.01279i 0.809832 + 0.541112i 0.890156 0.455656i \(-0.150595\pi\)
−0.0803237 + 0.996769i \(0.525595\pi\)
\(32\) 0.382683 + 0.923880i 0.0676495 + 0.163320i
\(33\) 6.82817 + 6.82817i 1.18863 + 1.18863i
\(34\) 1.12028 + 3.96799i 0.192127 + 0.680505i
\(35\) 1.42198 + 3.29876i 0.240359 + 0.557592i
\(36\) −1.55130 + 3.74516i −0.258549 + 0.624194i
\(37\) 5.44865 1.08380i 0.895753 0.178176i 0.274315 0.961640i \(-0.411549\pi\)
0.621438 + 0.783464i \(0.286549\pi\)
\(38\) −5.94691 −0.964716
\(39\) −9.04734 + 1.79963i −1.44873 + 0.288171i
\(40\) 1.87679 + 1.21558i 0.296747 + 0.192201i
\(41\) 2.21131 11.1170i 0.345349 1.73619i −0.283782 0.958889i \(-0.591589\pi\)
0.629131 0.777299i \(-0.283411\pi\)
\(42\) −3.94184 1.63276i −0.608239 0.251941i
\(43\) 4.83901 + 2.00438i 0.737941 + 0.305665i 0.719811 0.694170i \(-0.244229\pi\)
0.0181306 + 0.999836i \(0.494229\pi\)
\(44\) −0.709326 + 3.56602i −0.106935 + 0.537598i
\(45\) 1.89531 + 8.86406i 0.282536 + 1.32138i
\(46\) 2.02929 0.403651i 0.299203 0.0595151i
\(47\) −1.43673 −0.209569 −0.104785 0.994495i \(-0.533415\pi\)
−0.104785 + 0.994495i \(0.533415\pi\)
\(48\) −2.60485 + 0.518138i −0.375978 + 0.0747867i
\(49\) −1.69117 + 4.08284i −0.241595 + 0.583263i
\(50\) 4.99796 0.142959i 0.706818 0.0202174i
\(51\) −10.9165 + 0.862208i −1.52862 + 0.120733i
\(52\) −2.45597 2.45597i −0.340581 0.340581i
\(53\) 3.14380 + 7.58981i 0.431834 + 1.04254i 0.978696 + 0.205317i \(0.0658226\pi\)
−0.546861 + 0.837223i \(0.684177\pi\)
\(54\) −2.32695 1.55482i −0.316658 0.211584i
\(55\) 3.21832 + 7.46597i 0.433958 + 1.00671i
\(56\) −0.313408 1.57561i −0.0418809 0.210549i
\(57\) 3.08132 15.4908i 0.408131 2.05181i
\(58\) 2.31960 + 3.47152i 0.304578 + 0.455833i
\(59\) −1.18771 2.86738i −0.154627 0.373302i 0.827515 0.561443i \(-0.189754\pi\)
−0.982142 + 0.188141i \(0.939754\pi\)
\(60\) −4.13886 + 4.25894i −0.534324 + 0.549826i
\(61\) 14.2603 + 2.83655i 1.82585 + 0.363183i 0.984230 0.176894i \(-0.0566051\pi\)
0.841615 + 0.540077i \(0.181605\pi\)
\(62\) −5.31867 1.05795i −0.675472 0.134360i
\(63\) 3.61800 5.41472i 0.455825 0.682190i
\(64\) −0.707107 0.707107i −0.0883883 0.0883883i
\(65\) −7.63810 1.40610i −0.947390 0.174405i
\(66\) −8.92144 3.69538i −1.09815 0.454870i
\(67\) −0.280368 + 0.280368i −0.0342524 + 0.0342524i −0.724026 0.689773i \(-0.757710\pi\)
0.689773 + 0.724026i \(0.257710\pi\)
\(68\) −2.55349 3.23723i −0.309656 0.392572i
\(69\) 5.49515i 0.661539i
\(70\) −2.57612 2.50349i −0.307905 0.299224i
\(71\) 8.39457 12.5634i 0.996252 1.49100i 0.129923 0.991524i \(-0.458527\pi\)
0.866329 0.499473i \(-0.166473\pi\)
\(72\) 4.05373i 0.477737i
\(73\) −2.74845 1.83646i −0.321682 0.214941i 0.384235 0.923235i \(-0.374465\pi\)
−0.705918 + 0.708294i \(0.749465\pi\)
\(74\) −4.61914 + 3.08641i −0.536965 + 0.358788i
\(75\) −2.21724 + 13.0930i −0.256025 + 1.51185i
\(76\) 5.49423 2.27578i 0.630231 0.261050i
\(77\) 2.23524 5.39634i 0.254729 0.614970i
\(78\) 7.66996 5.12490i 0.868452 0.580281i
\(79\) −8.99386 13.4603i −1.01189 1.51440i −0.849443 0.527681i \(-0.823062\pi\)
−0.162446 0.986717i \(-0.551938\pi\)
\(80\) −2.19912 0.404835i −0.245869 0.0452619i
\(81\) −3.34351 + 3.34351i −0.371501 + 0.371501i
\(82\) 2.21131 + 11.1170i 0.244199 + 1.22767i
\(83\) 5.82251 2.41176i 0.639104 0.264725i −0.0395117 0.999219i \(-0.512580\pi\)
0.678616 + 0.734494i \(0.262580\pi\)
\(84\) 4.26662 0.465526
\(85\) −8.80890 2.72089i −0.955460 0.295122i
\(86\) −5.23770 −0.564796
\(87\) −10.2447 + 4.24348i −1.09834 + 0.454949i
\(88\) −0.709326 3.56602i −0.0756144 0.380139i
\(89\) −3.47194 + 3.47194i −0.368025 + 0.368025i −0.866756 0.498732i \(-0.833799\pi\)
0.498732 + 0.866756i \(0.333799\pi\)
\(90\) −5.14317 7.46402i −0.542137 0.786777i
\(91\) 3.09992 + 4.63936i 0.324960 + 0.486337i
\(92\) −1.72035 + 1.14950i −0.179359 + 0.119844i
\(93\) 5.51161 13.3062i 0.571528 1.37979i
\(94\) 1.32737 0.549814i 0.136908 0.0567090i
\(95\) 7.22897 11.1611i 0.741676 1.14511i
\(96\) 2.20829 1.47553i 0.225383 0.150596i
\(97\) −1.67183 1.11708i −0.169749 0.113423i 0.467794 0.883838i \(-0.345049\pi\)
−0.637543 + 0.770415i \(0.720049\pi\)
\(98\) 4.41923i 0.446410i
\(99\) 8.18850 12.2550i 0.822975 1.23167i
\(100\) −4.56280 + 2.04471i −0.456280 + 0.204471i
\(101\) 9.43783i 0.939099i 0.882906 + 0.469550i \(0.155584\pi\)
−0.882906 + 0.469550i \(0.844416\pi\)
\(102\) 9.75558 4.97414i 0.965947 0.492513i
\(103\) −4.20253 + 4.20253i −0.414087 + 0.414087i −0.883160 0.469073i \(-0.844588\pi\)
0.469073 + 0.883160i \(0.344588\pi\)
\(104\) 3.20887 + 1.32916i 0.314656 + 0.130335i
\(105\) 7.85600 5.41326i 0.766667 0.528280i
\(106\) −5.80899 5.80899i −0.564219 0.564219i
\(107\) −7.54818 + 11.2966i −0.729710 + 1.09209i 0.262184 + 0.965018i \(0.415557\pi\)
−0.991894 + 0.127070i \(0.959443\pi\)
\(108\) 2.74482 + 0.545980i 0.264121 + 0.0525369i
\(109\) 9.32519 + 1.85490i 0.893191 + 0.177667i 0.620287 0.784375i \(-0.287016\pi\)
0.272904 + 0.962041i \(0.412016\pi\)
\(110\) −5.83044 5.66606i −0.555911 0.540237i
\(111\) −5.64631 13.6314i −0.535924 1.29383i
\(112\) 0.892510 + 1.33574i 0.0843343 + 0.126215i
\(113\) −3.89058 + 19.5593i −0.365995 + 1.83998i 0.156937 + 0.987609i \(0.449838\pi\)
−0.522932 + 0.852374i \(0.675162\pi\)
\(114\) 3.08132 + 15.4908i 0.288592 + 1.45085i
\(115\) −1.70920 + 4.29923i −0.159384 + 0.400906i
\(116\) −3.47152 2.31960i −0.322322 0.215369i
\(117\) 5.38806 + 13.0079i 0.498126 + 1.20258i
\(118\) 2.19460 + 2.19460i 0.202029 + 0.202029i
\(119\) 3.00873 + 5.90090i 0.275810 + 0.540934i
\(120\) 2.19398 5.51862i 0.200282 0.503778i
\(121\) 0.849425 2.05069i 0.0772204 0.186427i
\(122\) −14.2603 + 2.83655i −1.29107 + 0.256809i
\(123\) −30.1040 −2.71439
\(124\) 5.31867 1.05795i 0.477631 0.0950067i
\(125\) −5.80713 + 9.55391i −0.519406 + 0.854528i
\(126\) −1.27047 + 6.38710i −0.113183 + 0.569008i
\(127\) 6.65893 + 2.75822i 0.590885 + 0.244752i 0.658031 0.752991i \(-0.271389\pi\)
−0.0671465 + 0.997743i \(0.521389\pi\)
\(128\) 0.923880 + 0.382683i 0.0816602 + 0.0338248i
\(129\) 2.71385 13.6435i 0.238941 1.20124i
\(130\) 7.59477 1.62391i 0.666106 0.142426i
\(131\) −6.51122 + 1.29516i −0.568888 + 0.113159i −0.471150 0.882053i \(-0.656161\pi\)
−0.0977383 + 0.995212i \(0.531161\pi\)
\(132\) 9.65650 0.840490
\(133\) −9.37000 + 1.86381i −0.812482 + 0.161613i
\(134\) 0.151734 0.366318i 0.0131078 0.0316451i
\(135\) 5.74668 2.47719i 0.494595 0.213203i
\(136\) 3.59795 + 2.01363i 0.308522 + 0.172668i
\(137\) 5.32839 + 5.32839i 0.455235 + 0.455235i 0.897088 0.441852i \(-0.145679\pi\)
−0.441852 + 0.897088i \(0.645679\pi\)
\(138\) −2.10290 5.07686i −0.179011 0.432171i
\(139\) −15.6578 10.4622i −1.32808 0.887393i −0.329686 0.944091i \(-0.606943\pi\)
−0.998391 + 0.0566979i \(0.981943\pi\)
\(140\) 3.33807 + 1.32708i 0.282118 + 0.112159i
\(141\) 0.744426 + 3.74248i 0.0626920 + 0.315174i
\(142\) −2.94778 + 14.8195i −0.247372 + 1.24362i
\(143\) 7.01595 + 10.5001i 0.586703 + 0.878063i
\(144\) 1.55130 + 3.74516i 0.129275 + 0.312097i
\(145\) −9.33499 + 0.133479i −0.775229 + 0.0110848i
\(146\) 3.24202 + 0.644878i 0.268312 + 0.0533705i
\(147\) 11.5115 + 2.28977i 0.949450 + 0.188857i
\(148\) 3.08641 4.61914i 0.253702 0.379691i
\(149\) 12.9817 + 12.9817i 1.06350 + 1.06350i 0.997842 + 0.0656569i \(0.0209143\pi\)
0.0656569 + 0.997842i \(0.479086\pi\)
\(150\) −2.96202 12.9449i −0.241848 1.05694i
\(151\) −0.378610 0.156826i −0.0308109 0.0127623i 0.367225 0.930132i \(-0.380308\pi\)
−0.398036 + 0.917370i \(0.630308\pi\)
\(152\) −4.20510 + 4.20510i −0.341079 + 0.341079i
\(153\) 4.54133 + 16.0852i 0.367145 + 1.30041i
\(154\) 5.84096i 0.470678i
\(155\) 8.45085 8.69603i 0.678789 0.698482i
\(156\) −5.12490 + 7.66996i −0.410321 + 0.614088i
\(157\) 15.7933i 1.26044i −0.776417 0.630220i \(-0.782965\pi\)
0.776417 0.630220i \(-0.217035\pi\)
\(158\) 13.4603 + 8.99386i 1.07084 + 0.715513i
\(159\) 18.1414 12.1217i 1.43871 0.961314i
\(160\) 2.18664 0.467546i 0.172869 0.0369628i
\(161\) 3.07086 1.27199i 0.242018 0.100247i
\(162\) 1.80950 4.36851i 0.142167 0.343223i
\(163\) −7.16436 + 4.78707i −0.561156 + 0.374952i −0.803561 0.595223i \(-0.797064\pi\)
0.242405 + 0.970175i \(0.422064\pi\)
\(164\) −6.29729 9.42456i −0.491736 0.735934i
\(165\) 17.7802 12.2517i 1.38419 0.953790i
\(166\) −4.45636 + 4.45636i −0.345881 + 0.345881i
\(167\) 1.78233 + 8.96036i 0.137921 + 0.693373i 0.986429 + 0.164191i \(0.0525013\pi\)
−0.848508 + 0.529182i \(0.822499\pi\)
\(168\) −3.94184 + 1.63276i −0.304120 + 0.125970i
\(169\) 0.936468 0.0720360
\(170\) 9.17960 0.857250i 0.704043 0.0657480i
\(171\) −24.1072 −1.84352
\(172\) 4.83901 2.00438i 0.368971 0.152833i
\(173\) −0.622963 3.13185i −0.0473630 0.238110i 0.949851 0.312703i \(-0.101234\pi\)
−0.997214 + 0.0745927i \(0.976234\pi\)
\(174\) 7.84093 7.84093i 0.594420 0.594420i
\(175\) 7.83001 1.79165i 0.591893 0.135436i
\(176\) 2.01999 + 3.02313i 0.152262 + 0.227877i
\(177\) −6.85372 + 4.57951i −0.515157 + 0.344217i
\(178\) 1.87900 4.53631i 0.140837 0.340010i
\(179\) 7.13628 2.95594i 0.533390 0.220938i −0.0996970 0.995018i \(-0.531787\pi\)
0.633087 + 0.774080i \(0.281787\pi\)
\(180\) 7.60802 + 4.92765i 0.567069 + 0.367286i
\(181\) 13.5482 9.05259i 1.00703 0.672874i 0.0613952 0.998114i \(-0.480445\pi\)
0.945632 + 0.325240i \(0.105445\pi\)
\(182\) −4.63936 3.09992i −0.343892 0.229781i
\(183\) 38.6157i 2.85456i
\(184\) 1.14950 1.72035i 0.0847423 0.126826i
\(185\) −0.177605 12.4210i −0.0130578 0.913208i
\(186\) 14.4025i 1.05605i
\(187\) 6.80955 + 13.3553i 0.497964 + 0.976636i
\(188\) −1.01592 + 1.01592i −0.0740939 + 0.0740939i
\(189\) −4.15365 1.72050i −0.302134 0.125148i
\(190\) −2.40752 + 13.0779i −0.174660 + 0.948774i
\(191\) 1.57174 + 1.57174i 0.113727 + 0.113727i 0.761680 0.647953i \(-0.224375\pi\)
−0.647953 + 0.761680i \(0.724375\pi\)
\(192\) −1.47553 + 2.20829i −0.106487 + 0.159370i
\(193\) −6.72471 1.33763i −0.484055 0.0962845i −0.0529705 0.998596i \(-0.516869\pi\)
−0.431084 + 0.902312i \(0.641869\pi\)
\(194\) 1.97206 + 0.392268i 0.141586 + 0.0281632i
\(195\) 0.294908 + 20.6247i 0.0211188 + 1.47696i
\(196\) 1.69117 + 4.08284i 0.120798 + 0.291631i
\(197\) −6.49763 9.72440i −0.462937 0.692835i 0.524400 0.851472i \(-0.324290\pi\)
−0.987337 + 0.158638i \(0.949290\pi\)
\(198\) −2.87542 + 14.4557i −0.204347 + 1.02732i
\(199\) 2.74607 + 13.8054i 0.194663 + 0.978639i 0.947335 + 0.320243i \(0.103765\pi\)
−0.752672 + 0.658396i \(0.771235\pi\)
\(200\) 3.43300 3.63518i 0.242750 0.257046i
\(201\) 0.875587 + 0.585048i 0.0617591 + 0.0412661i
\(202\) −3.61170 8.71942i −0.254118 0.613496i
\(203\) 4.74277 + 4.74277i 0.332877 + 0.332877i
\(204\) −7.10946 + 8.32881i −0.497762 + 0.583133i
\(205\) −23.5524 9.36350i −1.64497 0.653975i
\(206\) 2.27439 5.49086i 0.158464 0.382567i
\(207\) 8.22621 1.63629i 0.571761 0.113730i
\(208\) −3.47326 −0.240827
\(209\) −21.2068 + 4.21830i −1.46691 + 0.291786i
\(210\) −5.18643 + 8.00756i −0.357898 + 0.552574i
\(211\) −1.20610 + 6.06350i −0.0830317 + 0.417428i 0.916805 + 0.399336i \(0.130759\pi\)
−0.999836 + 0.0180924i \(0.994241\pi\)
\(212\) 7.58981 + 3.14380i 0.521270 + 0.215917i
\(213\) −37.0753 15.3571i −2.54036 1.05225i
\(214\) 2.65057 13.3253i 0.181189 0.910899i
\(215\) 6.36687 9.83009i 0.434217 0.670406i
\(216\) −2.74482 + 0.545980i −0.186762 + 0.0371492i
\(217\) −8.71172 −0.591390
\(218\) −9.32519 + 1.85490i −0.631582 + 0.125629i
\(219\) −3.35963 + 8.11086i −0.227023 + 0.548081i
\(220\) 7.55493 + 3.00354i 0.509353 + 0.202499i
\(221\) −14.2218 1.67925i −0.956663 0.112958i
\(222\) 10.4330 + 10.4330i 0.700218 + 0.700218i
\(223\) 4.21177 + 10.1681i 0.282041 + 0.680907i 0.999883 0.0152988i \(-0.00486996\pi\)
−0.717842 + 0.696206i \(0.754870\pi\)
\(224\) −1.33574 0.892510i −0.0892476 0.0596333i
\(225\) 20.2604 0.579517i 1.35069 0.0386344i
\(226\) −3.89058 19.5593i −0.258798 1.30106i
\(227\) 0.864666 4.34697i 0.0573899 0.288519i −0.941423 0.337228i \(-0.890511\pi\)
0.998813 + 0.0487092i \(0.0155108\pi\)
\(228\) −8.77485 13.1325i −0.581129 0.869721i
\(229\) −0.0300817 0.0726235i −0.00198785 0.00479910i 0.922882 0.385082i \(-0.125827\pi\)
−0.924870 + 0.380283i \(0.875827\pi\)
\(230\) −0.0661470 4.62606i −0.00436161 0.305033i
\(231\) −15.2149 3.02642i −1.00106 0.199124i
\(232\) 4.09494 + 0.814533i 0.268846 + 0.0534767i
\(233\) 4.43713 6.64063i 0.290686 0.435042i −0.657170 0.753743i \(-0.728246\pi\)
0.947855 + 0.318701i \(0.103246\pi\)
\(234\) −9.95583 9.95583i −0.650833 0.650833i
\(235\) −0.581640 + 3.15954i −0.0379420 + 0.206106i
\(236\) −2.86738 1.18771i −0.186651 0.0773133i
\(237\) −30.4020 + 30.4020i −1.97482 + 1.97482i
\(238\) −5.03788 4.30033i −0.326557 0.278749i
\(239\) 0.721014i 0.0466385i 0.999728 + 0.0233193i \(0.00742342\pi\)
−0.999728 + 0.0233193i \(0.992577\pi\)
\(240\) 0.0849082 + 5.93814i 0.00548080 + 0.383305i
\(241\) −6.85427 + 10.2581i −0.441522 + 0.660785i −0.983770 0.179434i \(-0.942573\pi\)
0.542248 + 0.840219i \(0.317573\pi\)
\(242\) 2.21965i 0.142685i
\(243\) 17.4226 + 11.6414i 1.11766 + 0.746797i
\(244\) 12.0893 8.07781i 0.773938 0.517129i
\(245\) 8.29399 + 5.37195i 0.529884 + 0.343201i
\(246\) 27.8125 11.5203i 1.77326 0.734508i
\(247\) 7.90439 19.0829i 0.502944 1.21421i
\(248\) −4.50895 + 3.01279i −0.286319 + 0.191312i
\(249\) −9.29916 13.9172i −0.589310 0.881965i
\(250\) 1.70897 11.0490i 0.108084 0.698797i
\(251\) 9.36064 9.36064i 0.590838 0.590838i −0.347020 0.937858i \(-0.612806\pi\)
0.937858 + 0.347020i \(0.112806\pi\)
\(252\) −1.27047 6.38710i −0.0800322 0.402349i
\(253\) 6.95018 2.87886i 0.436954 0.180992i
\(254\) −7.20758 −0.452244
\(255\) −2.52329 + 24.3557i −0.158014 + 1.52521i
\(256\) −1.00000 −0.0625000
\(257\) 4.15967 1.72299i 0.259473 0.107477i −0.249155 0.968464i \(-0.580153\pi\)
0.508628 + 0.860986i \(0.330153\pi\)
\(258\) 2.71385 + 13.6435i 0.168957 + 0.849404i
\(259\) −6.31065 + 6.31065i −0.392125 + 0.392125i
\(260\) −6.39521 + 4.40669i −0.396614 + 0.273291i
\(261\) 9.40302 + 14.0726i 0.582032 + 0.871073i
\(262\) 5.51995 3.68831i 0.341023 0.227865i
\(263\) 1.54344 3.72618i 0.0951724 0.229766i −0.869123 0.494596i \(-0.835316\pi\)
0.964295 + 0.264830i \(0.0853159\pi\)
\(264\) −8.92144 + 3.69538i −0.549077 + 0.227435i
\(265\) 17.9636 3.84096i 1.10349 0.235948i
\(266\) 7.94350 5.30768i 0.487047 0.325435i
\(267\) 10.8428 + 7.24495i 0.663571 + 0.443384i
\(268\) 0.396500i 0.0242201i
\(269\) −5.06374 + 7.57842i −0.308741 + 0.462064i −0.953098 0.302661i \(-0.902125\pi\)
0.644357 + 0.764725i \(0.277125\pi\)
\(270\) −4.36126 + 4.48779i −0.265418 + 0.273118i
\(271\) 16.0423i 0.974499i −0.873263 0.487249i \(-0.838000\pi\)
0.873263 0.487249i \(-0.162000\pi\)
\(272\) −4.09466 0.483478i −0.248275 0.0293152i
\(273\) 10.4787 10.4787i 0.634198 0.634198i
\(274\) −6.96188 2.88371i −0.420583 0.174211i
\(275\) 17.7214 4.05497i 1.06864 0.244524i
\(276\) 3.88566 + 3.88566i 0.233889 + 0.233889i
\(277\) 12.6202 18.8874i 0.758272 1.13483i −0.228629 0.973514i \(-0.573424\pi\)
0.986902 0.161321i \(-0.0515756\pi\)
\(278\) 18.4696 + 3.67384i 1.10773 + 0.220342i
\(279\) −21.5605 4.28865i −1.29079 0.256755i
\(280\) −3.59182 + 0.0513587i −0.214652 + 0.00306927i
\(281\) −3.11925 7.53054i −0.186079 0.449235i 0.803119 0.595818i \(-0.203172\pi\)
−0.989198 + 0.146584i \(0.953172\pi\)
\(282\) −2.11995 3.17272i −0.126241 0.188933i
\(283\) −3.63237 + 18.2612i −0.215922 + 1.08551i 0.708957 + 0.705252i \(0.249166\pi\)
−0.924879 + 0.380261i \(0.875834\pi\)
\(284\) −2.94778 14.8195i −0.174919 0.879375i
\(285\) −32.8187 13.0474i −1.94401 0.772862i
\(286\) −10.5001 7.01595i −0.620884 0.414862i
\(287\) 6.96833 + 16.8230i 0.411327 + 0.993032i
\(288\) −2.86642 2.86642i −0.168906 0.168906i
\(289\) −16.5325 3.95936i −0.972500 0.232903i
\(290\) 8.57333 3.69566i 0.503443 0.217017i
\(291\) −2.04360 + 4.93369i −0.119798 + 0.289218i
\(292\) −3.24202 + 0.644878i −0.189725 + 0.0377387i
\(293\) 19.8193 1.15786 0.578929 0.815378i \(-0.303471\pi\)
0.578929 + 0.815378i \(0.303471\pi\)
\(294\) −11.5115 + 2.28977i −0.671362 + 0.133542i
\(295\) −6.78654 + 1.45109i −0.395127 + 0.0844859i
\(296\) −1.08380 + 5.44865i −0.0629948 + 0.316696i
\(297\) −9.40083 3.89395i −0.545491 0.225950i
\(298\) −16.9614 7.02562i −0.982545 0.406984i
\(299\) −1.40198 + 7.04825i −0.0810789 + 0.407611i
\(300\) 7.69034 + 10.8260i 0.444002 + 0.625039i
\(301\) −8.25256 + 1.64154i −0.475670 + 0.0946166i
\(302\) 0.409805 0.0235816
\(303\) 24.5842 4.89010i 1.41232 0.280929i
\(304\) 2.27578 5.49423i 0.130525 0.315116i
\(305\) 12.0110 30.2117i 0.687747 1.72992i
\(306\) −10.3512 13.1229i −0.591737 0.750185i
\(307\) −7.70417 7.70417i −0.439700 0.439700i 0.452211 0.891911i \(-0.350635\pi\)
−0.891911 + 0.452211i \(0.850635\pi\)
\(308\) −2.23524 5.39634i −0.127365 0.307485i
\(309\) 13.1245 + 8.76948i 0.746624 + 0.498878i
\(310\) −4.47974 + 11.2681i −0.254432 + 0.639984i
\(311\) 2.13288 + 10.7227i 0.120944 + 0.608029i 0.992950 + 0.118533i \(0.0378191\pi\)
−0.872006 + 0.489496i \(0.837181\pi\)
\(312\) 1.79963 9.04734i 0.101884 0.512205i
\(313\) −3.21682 4.81431i −0.181825 0.272121i 0.729349 0.684142i \(-0.239823\pi\)
−0.911174 + 0.412021i \(0.864823\pi\)
\(314\) 6.04382 + 14.5911i 0.341073 + 0.823422i
\(315\) −10.4429 10.1485i −0.588391 0.571801i
\(316\) −15.8775 3.15822i −0.893177 0.177664i
\(317\) 0.112281 + 0.0223341i 0.00630633 + 0.00125441i 0.198242 0.980153i \(-0.436477\pi\)
−0.191936 + 0.981407i \(0.561477\pi\)
\(318\) −12.1217 + 18.1414i −0.679752 + 1.01732i
\(319\) 10.7342 + 10.7342i 0.600998 + 0.600998i
\(320\) −1.84127 + 1.26875i −0.102930 + 0.0709252i
\(321\) 33.3371 + 13.8087i 1.86070 + 0.770726i
\(322\) −2.35033 + 2.35033i −0.130979 + 0.130979i
\(323\) 11.9749 21.3967i 0.666301 1.19054i
\(324\) 4.72844i 0.262691i
\(325\) −6.18434 + 16.2278i −0.343046 + 0.900158i
\(326\) 4.78707 7.16436i 0.265131 0.396797i
\(327\) 25.2519i 1.39643i
\(328\) 9.42456 + 6.29729i 0.520384 + 0.347710i
\(329\) 1.91910 1.28230i 0.105803 0.0706955i
\(330\) −11.7383 + 18.1233i −0.646171 + 0.997652i
\(331\) −26.2403 + 10.8691i −1.44230 + 0.597419i −0.960354 0.278784i \(-0.910069\pi\)
−0.481942 + 0.876203i \(0.660069\pi\)
\(332\) 2.41176 5.82251i 0.132363 0.319552i
\(333\) −18.7248 + 12.5115i −1.02611 + 0.685626i
\(334\) −5.07563 7.59622i −0.277726 0.415647i
\(335\) 0.503059 + 0.730064i 0.0274850 + 0.0398877i
\(336\) 3.01695 3.01695i 0.164588 0.164588i
\(337\) 6.09727 + 30.6530i 0.332139 + 1.66978i 0.680754 + 0.732512i \(0.261652\pi\)
−0.348615 + 0.937266i \(0.613348\pi\)
\(338\) −0.865184 + 0.358371i −0.0470598 + 0.0194928i
\(339\) 52.9650 2.87666
\(340\) −8.15279 + 4.30488i −0.442147 + 0.233465i
\(341\) −19.7169 −1.06773
\(342\) 22.2721 9.22542i 1.20434 0.498854i
\(343\) −3.57888 17.9922i −0.193241 0.971490i
\(344\) −3.70361 + 3.70361i −0.199685 + 0.199685i
\(345\) 12.0845 + 2.22463i 0.650606 + 0.119770i
\(346\) 1.77405 + 2.65505i 0.0953735 + 0.142736i
\(347\) 12.7280 8.50457i 0.683274 0.456549i −0.164870 0.986315i \(-0.552720\pi\)
0.848144 + 0.529766i \(0.177720\pi\)
\(348\) −4.24348 + 10.2447i −0.227475 + 0.549172i
\(349\) 14.0645 5.82573i 0.752858 0.311844i 0.0269509 0.999637i \(-0.491420\pi\)
0.725907 + 0.687793i \(0.241420\pi\)
\(350\) −6.54836 + 4.65168i −0.350024 + 0.248643i
\(351\) 8.08210 5.40029i 0.431391 0.288246i
\(352\) −3.02313 2.01999i −0.161133 0.107666i
\(353\) 19.1306i 1.01822i 0.860701 + 0.509110i \(0.170025\pi\)
−0.860701 + 0.509110i \(0.829975\pi\)
\(354\) 4.57951 6.85372i 0.243398 0.364271i
\(355\) −24.2299 23.5467i −1.28599 1.24973i
\(356\) 4.91006i 0.260233i
\(357\) 13.8120 10.8948i 0.731011 0.576613i
\(358\) −5.46187 + 5.46187i −0.288669 + 0.288669i
\(359\) −22.7964 9.44258i −1.20315 0.498360i −0.311133 0.950366i \(-0.600709\pi\)
−0.892015 + 0.452006i \(0.850709\pi\)
\(360\) −8.91463 1.64109i −0.469842 0.0864932i
\(361\) 11.5723 + 11.5723i 0.609070 + 0.609070i
\(362\) −9.05259 + 13.5482i −0.475794 + 0.712075i
\(363\) −5.78188 1.15009i −0.303470 0.0603639i
\(364\) 5.47250 + 1.08855i 0.286837 + 0.0570554i
\(365\) −5.15125 + 5.30070i −0.269629 + 0.277452i
\(366\) 14.7776 + 35.6763i 0.772438 + 1.86483i
\(367\) −1.10504 1.65382i −0.0576829 0.0863285i 0.801507 0.597985i \(-0.204032\pi\)
−0.859190 + 0.511657i \(0.829032\pi\)
\(368\) −0.403651 + 2.02929i −0.0210418 + 0.105784i
\(369\) 8.96408 + 45.0655i 0.466651 + 2.34601i
\(370\) 4.91739 + 11.4075i 0.255643 + 0.593049i
\(371\) −10.9733 7.33211i −0.569704 0.380664i
\(372\) −5.51161 13.3062i −0.285764 0.689895i
\(373\) −13.1540 13.1540i −0.681086 0.681086i 0.279159 0.960245i \(-0.409944\pi\)
−0.960245 + 0.279159i \(0.909944\pi\)
\(374\) −11.4021 9.73279i −0.589587 0.503270i
\(375\) 27.8954 + 10.1765i 1.44051 + 0.525512i
\(376\) 0.549814 1.32737i 0.0283545 0.0684538i
\(377\) −14.2228 + 2.82909i −0.732510 + 0.145705i
\(378\) 4.49588 0.231243
\(379\) 32.3617 6.43713i 1.66231 0.330653i 0.727580 0.686022i \(-0.240645\pi\)
0.934726 + 0.355369i \(0.115645\pi\)
\(380\) −2.78045 13.0038i −0.142634 0.667079i
\(381\) 3.73452 18.7747i 0.191325 0.961856i
\(382\) −2.05358 0.850619i −0.105070 0.0435214i
\(383\) 32.9607 + 13.6528i 1.68421 + 0.697624i 0.999513 0.0312000i \(-0.00993290\pi\)
0.684701 + 0.728824i \(0.259933\pi\)
\(384\) 0.518138 2.60485i 0.0264411 0.132928i
\(385\) −10.9623 7.10018i −0.558690 0.361859i
\(386\) 6.72471 1.33763i 0.342279 0.0680834i
\(387\) −21.2323 −1.07930
\(388\) −1.97206 + 0.392268i −0.100116 + 0.0199144i
\(389\) −6.47393 + 15.6295i −0.328241 + 0.792445i 0.670482 + 0.741926i \(0.266087\pi\)
−0.998723 + 0.0505188i \(0.983913\pi\)
\(390\) −8.16519 18.9419i −0.413460 0.959159i
\(391\) −2.63393 + 8.11410i −0.133204 + 0.410348i
\(392\) −3.12487 3.12487i −0.157830 0.157830i
\(393\) 6.74742 + 16.2897i 0.340362 + 0.821707i
\(394\) 9.72440 + 6.49763i 0.489908 + 0.327346i
\(395\) −33.2417 + 14.3294i −1.67257 + 0.720988i
\(396\) −2.87542 14.4557i −0.144495 0.726426i
\(397\) 0.858028 4.31360i 0.0430632 0.216493i −0.953262 0.302145i \(-0.902297\pi\)
0.996325 + 0.0856518i \(0.0272973\pi\)
\(398\) −7.82013 11.7037i −0.391988 0.586651i
\(399\) 9.70990 + 23.4418i 0.486103 + 1.17356i
\(400\) −1.78056 + 4.67222i −0.0890279 + 0.233611i
\(401\) 23.2855 + 4.63178i 1.16282 + 0.231300i 0.738527 0.674223i \(-0.235522\pi\)
0.424296 + 0.905523i \(0.360522\pi\)
\(402\) −1.03283 0.205442i −0.0515126 0.0102465i
\(403\) 10.4642 15.6608i 0.521258 0.780118i
\(404\) 6.67355 + 6.67355i 0.332022 + 0.332022i
\(405\) 5.99920 + 8.70634i 0.298103 + 0.432622i
\(406\) −6.19673 2.56677i −0.307539 0.127387i
\(407\) −14.2827 + 14.2827i −0.707967 + 0.707967i
\(408\) 3.38099 10.4155i 0.167384 0.515644i
\(409\) 13.2242i 0.653894i 0.945043 + 0.326947i \(0.106020\pi\)
−0.945043 + 0.326947i \(0.893980\pi\)
\(410\) 25.3428 0.362372i 1.25159 0.0178963i
\(411\) 11.1188 16.6405i 0.548452 0.820817i
\(412\) 5.94327i 0.292804i
\(413\) 4.14564 + 2.77003i 0.203993 + 0.136304i
\(414\) −6.97384 + 4.65977i −0.342746 + 0.229015i
\(415\) −2.94659 13.7807i −0.144642 0.676470i
\(416\) 3.20887 1.32916i 0.157328 0.0651674i
\(417\) −19.1396 + 46.2072i −0.937272 + 2.26277i
\(418\) 17.9783 12.0127i 0.879346 0.587560i
\(419\) −4.26857 6.38836i −0.208533 0.312092i 0.712429 0.701744i \(-0.247595\pi\)
−0.920962 + 0.389652i \(0.872595\pi\)
\(420\) 1.72728 9.38279i 0.0842825 0.457833i
\(421\) −5.96878 + 5.96878i −0.290901 + 0.290901i −0.837436 0.546535i \(-0.815946\pi\)
0.546535 + 0.837436i \(0.315946\pi\)
\(422\) −1.20610 6.06350i −0.0587123 0.295166i
\(423\) 5.38080 2.22880i 0.261624 0.108368i
\(424\) −8.21515 −0.398963
\(425\) −9.54970 + 18.2703i −0.463228 + 0.886239i
\(426\) 40.1300 1.94430
\(427\) −21.5797 + 8.93859i −1.04431 + 0.432568i
\(428\) 2.65057 + 13.3253i 0.128120 + 0.644103i
\(429\) 23.7160 23.7160i 1.14502 1.14502i
\(430\) −2.12041 + 11.5183i −0.102255 + 0.555462i
\(431\) 4.82911 + 7.22727i 0.232610 + 0.348125i 0.929351 0.369197i \(-0.120367\pi\)
−0.696741 + 0.717323i \(0.745367\pi\)
\(432\) 2.32695 1.55482i 0.111955 0.0748062i
\(433\) 2.36618 5.71245i 0.113711 0.274523i −0.856771 0.515698i \(-0.827533\pi\)
0.970482 + 0.241175i \(0.0775327\pi\)
\(434\) 8.04858 3.33383i 0.386344 0.160029i
\(435\) 5.18450 + 24.2471i 0.248578 + 1.16256i
\(436\) 7.90551 5.28230i 0.378605 0.252976i
\(437\) −10.2308 6.83598i −0.489404 0.327009i
\(438\) 8.77913i 0.419483i
\(439\) 9.38882 14.0514i 0.448104 0.670635i −0.536805 0.843706i \(-0.680369\pi\)
0.984909 + 0.173071i \(0.0553690\pi\)
\(440\) −8.12925 + 0.116239i −0.387547 + 0.00554145i
\(441\) 17.9144i 0.853067i
\(442\) 13.7819 3.89103i 0.655537 0.185078i
\(443\) 8.31892 8.31892i 0.395244 0.395244i −0.481308 0.876552i \(-0.659838\pi\)
0.876552 + 0.481308i \(0.159838\pi\)
\(444\) −13.6314 5.64631i −0.646917 0.267962i
\(445\) 6.22963 + 9.04075i 0.295313 + 0.428573i
\(446\) −7.78234 7.78234i −0.368504 0.368504i
\(447\) 27.0891 40.5416i 1.28127 1.91755i
\(448\) 1.57561 + 0.313408i 0.0744405 + 0.0148071i
\(449\) −0.743527 0.147897i −0.0350892 0.00697968i 0.177515 0.984118i \(-0.443194\pi\)
−0.212604 + 0.977139i \(0.568194\pi\)
\(450\) −18.4964 + 8.28872i −0.871928 + 0.390734i
\(451\) 15.7712 + 38.0750i 0.742636 + 1.79288i
\(452\) 11.0794 + 16.5816i 0.521133 + 0.779931i
\(453\) −0.212335 + 1.06748i −0.00997639 + 0.0501547i
\(454\) 0.864666 + 4.34697i 0.0405808 + 0.204013i
\(455\) 11.4574 4.93891i 0.537133 0.231540i
\(456\) 13.1325 + 8.77485i 0.614985 + 0.410920i
\(457\) −11.5518 27.8886i −0.540372 1.30457i −0.924461 0.381278i \(-0.875484\pi\)
0.384088 0.923296i \(-0.374516\pi\)
\(458\) 0.0555836 + 0.0555836i 0.00259725 + 0.00259725i
\(459\) 10.2798 5.24142i 0.479820 0.244649i
\(460\) 1.83143 + 4.24861i 0.0853907 + 0.198092i
\(461\) 3.34439 8.07407i 0.155764 0.376047i −0.826663 0.562698i \(-0.809763\pi\)
0.982426 + 0.186651i \(0.0597634\pi\)
\(462\) 15.2149 3.02642i 0.707859 0.140802i
\(463\) −15.9817 −0.742734 −0.371367 0.928486i \(-0.621111\pi\)
−0.371367 + 0.928486i \(0.621111\pi\)
\(464\) −4.09494 + 0.814533i −0.190103 + 0.0378138i
\(465\) −27.0306 17.5075i −1.25351 0.811890i
\(466\) −1.55811 + 7.83316i −0.0721781 + 0.362864i
\(467\) −38.5196 15.9553i −1.78247 0.738325i −0.992062 0.125751i \(-0.959866\pi\)
−0.790413 0.612574i \(-0.790134\pi\)
\(468\) 13.0079 + 5.38806i 0.601291 + 0.249063i
\(469\) 0.124266 0.624729i 0.00573808 0.0288473i
\(470\) −0.671740 3.14162i −0.0309850 0.144912i
\(471\) −41.1392 + 8.18309i −1.89559 + 0.377057i
\(472\) 3.10363 0.142856
\(473\) −18.6778 + 3.71524i −0.858804 + 0.170827i
\(474\) 16.4534 39.7221i 0.755731 1.82450i
\(475\) −21.6181 20.4157i −0.991905 0.936739i
\(476\) 6.30005 + 2.04507i 0.288763 + 0.0937357i
\(477\) −23.5481 23.5481i −1.07819 1.07819i
\(478\) −0.275920 0.666130i −0.0126203 0.0304681i
\(479\) −33.7108 22.5249i −1.54029 1.02919i −0.979552 0.201191i \(-0.935519\pi\)
−0.560735 0.827995i \(-0.689481\pi\)
\(480\) −2.35087 5.45363i −0.107302 0.248923i
\(481\) −3.76433 18.9246i −0.171639 0.862887i
\(482\) 2.40690 12.1003i 0.109631 0.551154i
\(483\) −4.90448 7.34008i −0.223162 0.333985i
\(484\) −0.849425 2.05069i −0.0386102 0.0932133i
\(485\) −3.13341 + 3.22432i −0.142281 + 0.146409i
\(486\) −20.5514 4.08792i −0.932229 0.185432i
\(487\) −16.0683 3.19619i −0.728125 0.144833i −0.182910 0.983130i \(-0.558552\pi\)
−0.545214 + 0.838297i \(0.683552\pi\)
\(488\) −8.07781 + 12.0893i −0.365665 + 0.547257i
\(489\) 16.1818 + 16.1818i 0.731764 + 0.731764i
\(490\) −9.71841 1.78906i −0.439033 0.0808216i
\(491\) 34.9175 + 14.4633i 1.57581 + 0.652720i 0.987742 0.156095i \(-0.0498906\pi\)
0.588063 + 0.808815i \(0.299891\pi\)
\(492\) −21.2867 + 21.2867i −0.959680 + 0.959680i
\(493\) −17.1612 + 1.35543i −0.772901 + 0.0610453i
\(494\) 20.6552i 0.929320i
\(495\) −23.6351 22.9687i −1.06232 1.03237i
\(496\) 3.01279 4.50895i 0.135278 0.202458i
\(497\) 24.2736i 1.08882i
\(498\) 13.9172 + 9.29916i 0.623644 + 0.416705i
\(499\) −24.3202 + 16.2502i −1.08872 + 0.727460i −0.964311 0.264771i \(-0.914704\pi\)
−0.124409 + 0.992231i \(0.539704\pi\)
\(500\) 2.64937 + 10.8619i 0.118484 + 0.485759i
\(501\) 22.4169 9.28540i 1.00151 0.414841i
\(502\) −5.06594 + 12.2303i −0.226104 + 0.545863i
\(503\) 8.16470 5.45548i 0.364046 0.243248i −0.360071 0.932925i \(-0.617248\pi\)
0.724117 + 0.689677i \(0.242248\pi\)
\(504\) 3.61800 + 5.41472i 0.161159 + 0.241191i
\(505\) 20.7549 + 3.82076i 0.923580 + 0.170022i
\(506\) −5.31943 + 5.31943i −0.236478 + 0.236478i
\(507\) −0.485219 2.43936i −0.0215494 0.108336i
\(508\) 6.65893 2.75822i 0.295442 0.122376i
\(509\) 8.81683 0.390799 0.195400 0.980724i \(-0.437400\pi\)
0.195400 + 0.980724i \(0.437400\pi\)
\(510\) −6.98931 23.4674i −0.309492 1.03915i
\(511\) 5.31027 0.234912
\(512\) 0.923880 0.382683i 0.0408301 0.0169124i
\(513\) 3.24689 + 16.3232i 0.143354 + 0.720688i
\(514\) −3.18368 + 3.18368i −0.140426 + 0.140426i
\(515\) 7.54051 + 10.9432i 0.332275 + 0.482214i
\(516\) −7.72839 11.5664i −0.340224 0.509181i
\(517\) 4.34343 2.90219i 0.191024 0.127638i
\(518\) 3.41530 8.24527i 0.150060 0.362276i
\(519\) −7.83523 + 3.24546i −0.343928 + 0.142460i
\(520\) 4.22204 6.51859i 0.185149 0.285859i
\(521\) −32.3811 + 21.6364i −1.41864 + 0.947906i −0.419447 + 0.907780i \(0.637776\pi\)
−0.999195 + 0.0401267i \(0.987224\pi\)
\(522\) −14.0726 9.40302i −0.615942 0.411559i
\(523\) 27.9616i 1.22267i 0.791370 + 0.611337i \(0.209368\pi\)
−0.791370 + 0.611337i \(0.790632\pi\)
\(524\) −3.68831 + 5.51995i −0.161125 + 0.241140i
\(525\) −8.72400 19.4677i −0.380747 0.849641i
\(526\) 4.03319i 0.175856i
\(527\) 14.5163 17.0060i 0.632341 0.740794i
\(528\) 6.82817 6.82817i 0.297158 0.297158i
\(529\) −17.2941 7.16347i −0.751919 0.311455i
\(530\) −15.1263 + 10.4230i −0.657045 + 0.452744i
\(531\) 8.89633 + 8.89633i 0.386068 + 0.386068i
\(532\) −5.30768 + 7.94350i −0.230117 + 0.344394i
\(533\) −38.6123 7.68047i −1.67248 0.332678i
\(534\) −12.7900 2.54409i −0.553477 0.110093i
\(535\) 21.7869 + 21.1726i 0.941928 + 0.915371i
\(536\) −0.151734 0.366318i −0.00655391 0.0158225i
\(537\) −11.3974 17.0574i −0.491833 0.736080i
\(538\) 1.77815 8.93935i 0.0766614 0.385403i
\(539\) −3.13468 15.7591i −0.135020 0.678792i
\(540\) 2.31187 5.81515i 0.0994872 0.250244i
\(541\) −3.25353 2.17394i −0.139880 0.0934648i 0.483661 0.875255i \(-0.339307\pi\)
−0.623541 + 0.781790i \(0.714307\pi\)
\(542\) 6.13911 + 14.8211i 0.263697 + 0.636622i
\(543\) −30.6005 30.6005i −1.31319 1.31319i
\(544\) 3.96799 1.12028i 0.170126 0.0480318i
\(545\) 7.85429 19.7562i 0.336441 0.846264i
\(546\) −5.67101 + 13.6910i −0.242697 + 0.585922i
\(547\) 31.7088 6.30728i 1.35577 0.269680i 0.536895 0.843649i \(-0.319597\pi\)
0.818877 + 0.573969i \(0.194597\pi\)
\(548\) 7.53549 0.321900
\(549\) −57.8075 + 11.4986i −2.46716 + 0.490749i
\(550\) −14.8207 + 10.5280i −0.631956 + 0.448915i
\(551\) 4.84396 24.3522i 0.206360 1.03744i
\(552\) −5.07686 2.10290i −0.216086 0.0895056i
\(553\) 24.0269 + 9.95225i 1.02173 + 0.423213i
\(554\) −4.43161 + 22.2792i −0.188281 + 0.946554i
\(555\) −32.2628 + 6.89841i −1.36948 + 0.292821i
\(556\) −18.4696 + 3.67384i −0.783287 + 0.155805i
\(557\) 19.8490 0.841031 0.420516 0.907285i \(-0.361849\pi\)
0.420516 + 0.907285i \(0.361849\pi\)
\(558\) 21.5605 4.28865i 0.912728 0.181553i
\(559\) 6.96174 16.8071i 0.294450 0.710865i
\(560\) 3.29876 1.42198i 0.139398 0.0600896i
\(561\) 31.2603 24.6578i 1.31981 1.04105i
\(562\) 5.76363 + 5.76363i 0.243124 + 0.243124i
\(563\) 1.69576 + 4.09394i 0.0714679 + 0.172539i 0.955577 0.294742i \(-0.0952337\pi\)
−0.884109 + 0.467281i \(0.845234\pi\)
\(564\) 3.17272 + 2.11995i 0.133596 + 0.0892659i
\(565\) 41.4381 + 16.4741i 1.74331 + 0.693072i
\(566\) −3.63237 18.2612i −0.152680 0.767573i
\(567\) 1.48193 7.45017i 0.0622352 0.312878i
\(568\) 8.39457 + 12.5634i 0.352228 + 0.527147i
\(569\) −14.3682 34.6879i −0.602345 1.45419i −0.871160 0.490999i \(-0.836632\pi\)
0.268815 0.963192i \(-0.413368\pi\)
\(570\) 35.3136 0.504941i 1.47912 0.0211497i
\(571\) −1.76310 0.350702i −0.0737835 0.0146764i 0.158061 0.987429i \(-0.449476\pi\)
−0.231844 + 0.972753i \(0.574476\pi\)
\(572\) 12.3857 + 2.46367i 0.517873 + 0.103011i
\(573\) 3.27977 4.90853i 0.137014 0.205057i
\(574\) −12.8758 12.8758i −0.537425 0.537425i
\(575\) 8.76256 + 5.49922i 0.365424 + 0.229333i
\(576\) 3.74516 + 1.55130i 0.156048 + 0.0646374i
\(577\) 16.6066 16.6066i 0.691342 0.691342i −0.271185 0.962527i \(-0.587416\pi\)
0.962527 + 0.271185i \(0.0874156\pi\)
\(578\) 16.7892 2.66874i 0.698339 0.111005i
\(579\) 18.2100i 0.756780i
\(580\) −6.50645 + 6.69522i −0.270166 + 0.278004i
\(581\) −5.62482 + 8.41813i −0.233357 + 0.349243i
\(582\) 5.34018i 0.221358i
\(583\) −24.8354 16.5945i −1.02858 0.687275i
\(584\) 2.74845 1.83646i 0.113732 0.0759932i
\(585\) 30.7872 6.58290i 1.27289 0.272169i
\(586\) −18.3107 + 7.58453i −0.756407 + 0.313314i
\(587\) 6.45706 15.5887i 0.266511 0.643415i −0.732803 0.680441i \(-0.761788\pi\)
0.999314 + 0.0370256i \(0.0117883\pi\)
\(588\) 9.75895 6.52072i 0.402452 0.268910i
\(589\) 17.9168 + 26.8143i 0.738248 + 1.10487i
\(590\) 5.71463 3.93773i 0.235268 0.162114i
\(591\) −21.9640 + 21.9640i −0.903477 + 0.903477i
\(592\) −1.08380 5.44865i −0.0445441 0.223938i
\(593\) 8.11961 3.36325i 0.333432 0.138112i −0.209685 0.977769i \(-0.567244\pi\)
0.543117 + 0.839657i \(0.317244\pi\)
\(594\) 10.1754 0.417501
\(595\) 14.1948 4.22765i 0.581930 0.173317i
\(596\) 18.3588 0.752007
\(597\) 34.5382 14.3062i 1.41356 0.585514i
\(598\) −1.40198 7.04825i −0.0573314 0.288225i
\(599\) −3.25613 + 3.25613i −0.133042 + 0.133042i −0.770492 0.637450i \(-0.779989\pi\)
0.637450 + 0.770492i \(0.279989\pi\)
\(600\) −11.2479 7.05895i −0.459192 0.288180i
\(601\) −4.22267 6.31967i −0.172246 0.257785i 0.735295 0.677747i \(-0.237043\pi\)
−0.907542 + 0.419962i \(0.862043\pi\)
\(602\) 6.99619 4.67470i 0.285143 0.190527i
\(603\) 0.615089 1.48496i 0.0250484 0.0604721i
\(604\) −0.378610 + 0.156826i −0.0154054 + 0.00638114i
\(605\) −4.16583 2.69818i −0.169365 0.109696i
\(606\) −20.8415 + 13.9258i −0.846626 + 0.565698i
\(607\) −0.461370 0.308278i −0.0187264 0.0125126i 0.546172 0.837673i \(-0.316085\pi\)
−0.564898 + 0.825161i \(0.691085\pi\)
\(608\) 5.94691i 0.241179i
\(609\) 9.89683 14.8116i 0.401040 0.600198i
\(610\) 0.464831 + 32.5084i 0.0188205 + 1.31623i
\(611\) 4.99015i 0.201880i
\(612\) 14.5852 + 8.16274i 0.589570 + 0.329959i
\(613\) 30.8016 30.8016i 1.24407 1.24407i 0.285767 0.958299i \(-0.407752\pi\)
0.958299 0.285767i \(-0.0922483\pi\)
\(614\) 10.0660 + 4.16946i 0.406230 + 0.168266i
\(615\) −12.1872 + 66.2022i −0.491434 + 2.66953i
\(616\) 4.13018 + 4.13018i 0.166410 + 0.166410i
\(617\) −8.99779 + 13.4661i −0.362237 + 0.542126i −0.967163 0.254155i \(-0.918203\pi\)
0.604926 + 0.796282i \(0.293203\pi\)
\(618\) −15.4814 3.07943i −0.622751 0.123873i
\(619\) −30.3711 6.04118i −1.22072 0.242816i −0.457648 0.889133i \(-0.651308\pi\)
−0.763069 + 0.646318i \(0.776308\pi\)
\(620\) −0.173368 12.1247i −0.00696263 0.486939i
\(621\) −2.21590 5.34966i −0.0889211 0.214675i
\(622\) −6.07392 9.09027i −0.243542 0.364487i
\(623\) 1.53885 7.73633i 0.0616528 0.309950i
\(624\) 1.79963 + 9.04734i 0.0720427 + 0.362183i
\(625\) 18.6592 + 16.6383i 0.746369 + 0.665532i
\(626\) 4.81431 + 3.21682i 0.192418 + 0.128570i
\(627\) 21.9761 + 53.0550i 0.877641 + 2.11881i
\(628\) −11.1675 11.1675i −0.445633 0.445633i
\(629\) −1.80351 22.8344i −0.0719105 0.910466i
\(630\) 13.5316 + 5.37964i 0.539113 + 0.214330i
\(631\) 6.95969 16.8022i 0.277061 0.668885i −0.722691 0.691172i \(-0.757095\pi\)
0.999752 + 0.0222872i \(0.00709482\pi\)
\(632\) 15.8775 3.15822i 0.631572 0.125627i
\(633\) 16.4195 0.652615
\(634\) −0.112281 + 0.0223341i −0.00445925 + 0.000886999i
\(635\) 8.76141 13.5271i 0.347686 0.536808i
\(636\) 4.25658 21.3993i 0.168784 0.848536i
\(637\) 14.1808 + 5.87387i 0.561862 + 0.232731i
\(638\) −14.0249 5.80929i −0.555250 0.229992i
\(639\) −11.9495 + 60.0743i −0.472716 + 2.37650i
\(640\) 1.21558 1.87679i 0.0480502 0.0741868i
\(641\) −8.79233 + 1.74890i −0.347276 + 0.0690775i −0.365647 0.930754i \(-0.619152\pi\)
0.0183705 + 0.999831i \(0.494152\pi\)
\(642\) −36.0838 −1.42412
\(643\) −31.5973 + 6.28509i −1.24607 + 0.247860i −0.773708 0.633542i \(-0.781600\pi\)
−0.472367 + 0.881402i \(0.656600\pi\)
\(644\) 1.27199 3.07086i 0.0501235 0.121009i
\(645\) −28.9049 11.4914i −1.13813 0.452474i
\(646\) −2.87520 + 24.3506i −0.113123 + 0.958061i
\(647\) 5.46217 + 5.46217i 0.214740 + 0.214740i 0.806278 0.591537i \(-0.201479\pi\)
−0.591537 + 0.806278i \(0.701479\pi\)
\(648\) −1.80950 4.36851i −0.0710837 0.171611i
\(649\) 9.38268 + 6.26931i 0.368303 + 0.246092i
\(650\) −0.496533 17.3592i −0.0194756 0.680884i
\(651\) 4.51387 + 22.6928i 0.176912 + 0.889399i
\(652\) −1.68100 + 8.45094i −0.0658329 + 0.330964i
\(653\) 7.18766 + 10.7571i 0.281275 + 0.420958i 0.945026 0.326996i \(-0.106036\pi\)
−0.663751 + 0.747954i \(0.731036\pi\)
\(654\) 9.66347 + 23.3297i 0.377871 + 0.912262i
\(655\) 0.212241 + 14.8433i 0.00829293 + 0.579974i
\(656\) −11.1170 2.21131i −0.434047 0.0863373i
\(657\) 13.1423 + 2.61417i 0.512730 + 0.101988i
\(658\) −1.28230 + 1.91910i −0.0499893 + 0.0748142i
\(659\) 3.48601 + 3.48601i 0.135796 + 0.135796i 0.771737 0.635942i \(-0.219388\pi\)
−0.635942 + 0.771737i \(0.719388\pi\)
\(660\) 3.90929 21.2358i 0.152169 0.826600i
\(661\) 15.8424 + 6.56214i 0.616198 + 0.255238i 0.668876 0.743374i \(-0.266776\pi\)
−0.0526781 + 0.998612i \(0.516776\pi\)
\(662\) 20.0834 20.0834i 0.780565 0.780565i
\(663\) 2.99467 + 37.9159i 0.116303 + 1.47253i
\(664\) 6.30224i 0.244574i
\(665\) 0.305426 + 21.3602i 0.0118439 + 0.828315i
\(666\) 12.5115 18.7248i 0.484811 0.725571i
\(667\) 8.63860i 0.334488i
\(668\) 7.59622 + 5.07563i 0.293907 + 0.196382i
\(669\) 24.3042 16.2395i 0.939654 0.627857i
\(670\) −0.744149 0.481979i −0.0287490 0.0186205i
\(671\) −48.8405 + 20.2304i −1.88547 + 0.780986i
\(672\) −1.63276 + 3.94184i −0.0629852 + 0.152060i
\(673\) −23.2491 + 15.5346i −0.896188 + 0.598814i −0.916083 0.400988i \(-0.868667\pi\)
0.0198952 + 0.999802i \(0.493667\pi\)
\(674\) −17.3636 25.9864i −0.668819 1.00096i
\(675\) −3.12118 13.6405i −0.120134 0.525022i
\(676\) 0.662183 0.662183i 0.0254686 0.0254686i
\(677\) 4.47429 + 22.4938i 0.171961 + 0.864506i 0.966376 + 0.257131i \(0.0827773\pi\)
−0.794416 + 0.607375i \(0.792223\pi\)
\(678\) −48.9332 + 20.2688i −1.87927 + 0.778419i
\(679\) 3.23014 0.123961
\(680\) 5.88479 7.09713i 0.225672 0.272162i
\(681\) −11.7712 −0.451075
\(682\) 18.2161 7.54535i 0.697530 0.288926i
\(683\) 8.20130 + 41.2307i 0.313814 + 1.57765i 0.739740 + 0.672892i \(0.234948\pi\)
−0.425926 + 0.904758i \(0.640052\pi\)
\(684\) −17.0464 + 17.0464i −0.651784 + 0.651784i
\(685\) 13.8749 9.56063i 0.530132 0.365293i
\(686\) 10.1918 + 15.2531i 0.389124 + 0.582365i
\(687\) −0.173587 + 0.115987i −0.00662277 + 0.00442519i
\(688\) 2.00438 4.83901i 0.0764163 0.184485i
\(689\) 26.3614 10.9192i 1.00429 0.415990i
\(690\) −12.0159 + 2.56924i −0.457439 + 0.0978092i
\(691\) 17.3745 11.6093i 0.660956 0.441637i −0.179323 0.983790i \(-0.557391\pi\)
0.840280 + 0.542153i \(0.182391\pi\)
\(692\) −2.65505 1.77405i −0.100930 0.0674392i
\(693\) 23.6777i 0.899442i
\(694\) −8.50457 + 12.7280i −0.322829 + 0.483148i
\(695\) −29.3464 + 30.1978i −1.11317 + 1.14547i
\(696\) 11.0888i 0.420318i
\(697\) −44.4513 14.4294i −1.68371 0.546553i
\(698\) −10.7645 + 10.7645i −0.407444 + 0.407444i
\(699\) −19.5969 8.11731i −0.741224 0.307025i
\(700\) 4.26977 6.80354i 0.161382 0.257150i
\(701\) −24.8926 24.8926i −0.940182 0.940182i 0.0581274 0.998309i \(-0.481487\pi\)
−0.998309 + 0.0581274i \(0.981487\pi\)
\(702\) −5.40029 + 8.08210i −0.203821 + 0.305039i
\(703\) 32.4026 + 6.44529i 1.22209 + 0.243089i
\(704\) 3.56602 + 0.709326i 0.134399 + 0.0267337i
\(705\) 8.53152 0.121990i 0.321316 0.00459443i
\(706\) −7.32097 17.6744i −0.275528 0.665184i
\(707\) −8.42336 12.6064i −0.316793 0.474114i
\(708\) −1.60811 + 8.08452i −0.0604365 + 0.303835i
\(709\) 5.75229 + 28.9187i 0.216032 + 1.08606i 0.924751 + 0.380574i \(0.124273\pi\)
−0.708719 + 0.705491i \(0.750727\pi\)
\(710\) 31.3964 + 12.4820i 1.17829 + 0.468440i
\(711\) 54.5644 + 36.4587i 2.04632 + 1.36731i
\(712\) −1.87900 4.53631i −0.0704185 0.170005i
\(713\) −7.93386 7.93386i −0.297126 0.297126i
\(714\) −8.59141 + 15.3511i −0.321525 + 0.574500i
\(715\) 25.9312 11.1781i 0.969774 0.418036i
\(716\) 2.95594 7.13628i 0.110469 0.266695i
\(717\) 1.87814 0.373585i 0.0701403 0.0139518i
\(718\) 24.6747 0.920850
\(719\) −5.60952 + 1.11580i −0.209200 + 0.0416124i −0.298577 0.954385i \(-0.596512\pi\)
0.0893778 + 0.995998i \(0.471512\pi\)
\(720\) 8.86406 1.89531i 0.330344 0.0706340i
\(721\) 1.86267 9.36426i 0.0693694 0.348743i
\(722\) −15.1200 6.26290i −0.562707 0.233081i
\(723\) 30.2724 + 12.5393i 1.12584 + 0.466340i
\(724\) 3.17885 15.9811i 0.118141 0.593935i
\(725\) −3.48560 + 20.5828i −0.129452 + 0.764424i
\(726\) 5.78188 1.15009i 0.214586 0.0426837i
\(727\) −7.58102 −0.281165 −0.140582 0.990069i \(-0.544897\pi\)
−0.140582 + 0.990069i \(0.544897\pi\)
\(728\) −5.47250 + 1.08855i −0.202824 + 0.0403442i
\(729\) 15.8684 38.3097i 0.587719 1.41888i
\(730\) 2.73065 6.86851i 0.101066 0.254215i
\(731\) 10.5468 18.8450i 0.390088 0.697008i
\(732\) −27.3055 27.3055i −1.00924 1.00924i
\(733\) −2.14171 5.17054i −0.0791058 0.190978i 0.879379 0.476123i \(-0.157958\pi\)
−0.958484 + 0.285145i \(0.907958\pi\)
\(734\) 1.65382 + 1.10504i 0.0610435 + 0.0407879i
\(735\) 9.69572 24.3881i 0.357632 0.899567i
\(736\) −0.403651 2.02929i −0.0148788 0.0748007i
\(737\) 0.281248 1.41393i 0.0103599 0.0520827i
\(738\) −25.5275 38.2047i −0.939682 1.40633i
\(739\) 0.617255 + 1.49019i 0.0227061 + 0.0548174i 0.934826 0.355106i \(-0.115555\pi\)
−0.912120 + 0.409924i \(0.865555\pi\)
\(740\) −8.90854 8.65737i −0.327485 0.318251i
\(741\) −53.8037 10.7022i −1.97653 0.393156i
\(742\) 12.9439 + 2.57469i 0.475184 + 0.0945200i
\(743\) 11.6521 17.4387i 0.427475 0.639762i −0.553737 0.832691i \(-0.686799\pi\)
0.981213 + 0.192929i \(0.0617988\pi\)
\(744\) 10.1841 + 10.1841i 0.373368 + 0.373368i
\(745\) 33.8036 23.2927i 1.23847 0.853380i
\(746\) 17.1865 + 7.11887i 0.629242 + 0.260640i
\(747\) −18.0649 + 18.0649i −0.660960 + 0.660960i
\(748\) 14.2587 + 4.62854i 0.521350 + 0.169236i
\(749\) 21.8262i 0.797511i
\(750\) −29.6664 + 1.27328i −1.08326 + 0.0464935i
\(751\) 10.3739 15.5257i 0.378551 0.566541i −0.592453 0.805605i \(-0.701840\pi\)
0.971004 + 0.239064i \(0.0768405\pi\)
\(752\) 1.43673i 0.0523923i
\(753\) −29.2332 19.5330i −1.06532 0.711822i
\(754\) 12.0575 8.05656i 0.439108 0.293402i
\(755\) −0.498152 + 0.769119i −0.0181296 + 0.0279911i
\(756\) −4.15365 + 1.72050i −0.151067 + 0.0625740i
\(757\) −8.42597 + 20.3421i −0.306247 + 0.739346i 0.693573 + 0.720386i \(0.256035\pi\)
−0.999820 + 0.0189597i \(0.993965\pi\)
\(758\) −27.4349 + 18.3314i −0.996480 + 0.665827i
\(759\) −11.1002 16.6126i −0.402910 0.602997i
\(760\) 7.54513 + 10.9499i 0.273691 + 0.397194i
\(761\) 12.0277 12.0277i 0.436002 0.436002i −0.454662 0.890664i \(-0.650240\pi\)
0.890664 + 0.454662i \(0.150240\pi\)
\(762\) 3.73452 + 18.7747i 0.135287 + 0.680135i
\(763\) −14.1115 + 5.84518i −0.510871 + 0.211610i
\(764\) 2.22277 0.0804171
\(765\) 37.2117 3.47506i 1.34539 0.125641i
\(766\) −35.6764 −1.28904
\(767\) −9.95917 + 4.12522i −0.359605 + 0.148953i
\(768\) 0.518138 + 2.60485i 0.0186967 + 0.0939946i
\(769\) −3.88860 + 3.88860i −0.140227 + 0.140227i −0.773735 0.633509i \(-0.781614\pi\)
0.633509 + 0.773735i \(0.281614\pi\)
\(770\) 12.8449 + 2.36463i 0.462900 + 0.0852152i
\(771\) −6.64343 9.94259i −0.239257 0.358074i
\(772\) −5.70093 + 3.80924i −0.205181 + 0.137098i
\(773\) 3.46531 8.36601i 0.124639 0.300904i −0.849227 0.528027i \(-0.822932\pi\)
0.973866 + 0.227123i \(0.0729319\pi\)
\(774\) 19.6160 8.12523i 0.705084 0.292055i
\(775\) −15.7024 22.1048i −0.564046 0.794030i
\(776\) 1.67183 1.11708i 0.0600153 0.0401010i
\(777\) 19.7081 + 13.1685i 0.707025 + 0.472419i
\(778\) 16.9172i 0.606511i
\(779\) 37.4494 56.0470i 1.34176 2.00809i
\(780\) 14.7924 + 14.3753i 0.529652 + 0.514719i
\(781\) 54.9376i 1.96582i
\(782\) −0.671696 8.50441i −0.0240198 0.304117i
\(783\) 8.26226 8.26226i 0.295269 0.295269i
\(784\) 4.08284 + 1.69117i 0.145816 + 0.0603989i
\(785\) −34.7312 6.39367i −1.23961 0.228200i
\(786\) −12.4676 12.4676i −0.444705 0.444705i
\(787\) 8.00999 11.9878i 0.285525 0.427319i −0.660786 0.750574i \(-0.729777\pi\)
0.946312 + 0.323255i \(0.104777\pi\)
\(788\) −11.4707 2.28167i −0.408627 0.0812810i
\(789\) −10.5059 2.08975i −0.374019 0.0743971i
\(790\) 25.2277 25.9597i 0.897562 0.923603i
\(791\) −12.2601 29.5984i −0.435918 1.05240i
\(792\) 8.18850 + 12.2550i 0.290966 + 0.435461i
\(793\) 9.85208 49.5297i 0.349858 1.75885i
\(794\) 0.858028 + 4.31360i 0.0304503 + 0.153084i
\(795\) −19.3128 44.8024i −0.684953 1.58898i
\(796\) 11.7037 + 7.82013i 0.414825 + 0.277177i
\(797\) 8.52237 + 20.5748i 0.301878 + 0.728797i 0.999919 + 0.0127397i \(0.00405529\pi\)
−0.698041 + 0.716058i \(0.745945\pi\)
\(798\) −17.9416 17.9416i −0.635124 0.635124i
\(799\) −0.694630 + 5.88294i −0.0245742 + 0.208123i
\(800\) −0.142959 4.99796i −0.00505435 0.176704i
\(801\) 7.61696 18.3890i 0.269132 0.649743i
\(802\) −23.2855 + 4.63178i −0.822241 + 0.163554i
\(803\) 12.0186 0.424125
\(804\) 1.03283 0.205442i 0.0364249 0.00724537i
\(805\) −1.55406 7.26812i −0.0547736 0.256168i
\(806\) −3.67454 + 18.4731i −0.129430 + 0.650688i
\(807\) 22.3644 + 9.26363i 0.787264 + 0.326095i
\(808\) −8.71942 3.61170i −0.306748 0.127059i
\(809\) −6.87121 + 34.5439i −0.241579 + 1.21450i 0.649398 + 0.760449i \(0.275021\pi\)
−0.890976 + 0.454050i \(0.849979\pi\)
\(810\) −8.87431 5.74782i −0.311811 0.201958i
\(811\) 2.94357 0.585512i 0.103363 0.0205601i −0.143138 0.989703i \(-0.545719\pi\)
0.246501 + 0.969143i \(0.420719\pi\)
\(812\) 6.70730 0.235380
\(813\) −41.7878 + 8.31211i −1.46556 + 0.291518i
\(814\) 7.72974 18.6612i 0.270927 0.654076i
\(815\) 7.62694 + 17.6932i 0.267160 + 0.619767i
\(816\) 0.862208 + 10.9165i 0.0301833 + 0.382154i
\(817\) 22.0251 + 22.0251i 0.770559 + 0.770559i
\(818\) −5.06068 12.2176i −0.176943 0.427177i
\(819\) −18.8067 12.5663i −0.657160 0.439100i
\(820\) −23.2751 + 10.0331i −0.812800 + 0.350370i
\(821\) 8.73352 + 43.9064i 0.304802 + 1.53234i 0.764709 + 0.644376i \(0.222883\pi\)
−0.459906 + 0.887967i \(0.652117\pi\)
\(822\) −3.90442 + 19.6288i −0.136182 + 0.684635i
\(823\) 9.24436 + 13.8352i 0.322238 + 0.482264i 0.956856 0.290563i \(-0.0938425\pi\)
−0.634618 + 0.772826i \(0.718842\pi\)
\(824\) −2.27439 5.49086i −0.0792321 0.191283i
\(825\) −19.7447 44.0607i −0.687424 1.53400i
\(826\) −4.89011 0.972704i −0.170149 0.0338447i
\(827\) 45.2515 + 9.00109i 1.57355 + 0.312999i 0.903258 0.429099i \(-0.141169\pi\)
0.670292 + 0.742097i \(0.266169\pi\)
\(828\) 4.65977 6.97384i 0.161938 0.242358i
\(829\) −4.96498 4.96498i −0.172441 0.172441i 0.615610 0.788051i \(-0.288910\pi\)
−0.788051 + 0.615610i \(0.788910\pi\)
\(830\) 7.99596 + 11.6041i 0.277544 + 0.402786i
\(831\) −55.7380 23.0874i −1.93353 0.800894i
\(832\) −2.45597 + 2.45597i −0.0851453 + 0.0851453i
\(833\) 15.9002 + 8.89872i 0.550909 + 0.308323i
\(834\) 50.0143i 1.73185i
\(835\) 20.4264 0.292073i 0.706885 0.0101076i
\(836\) −12.0127 + 17.9783i −0.415468 + 0.621791i
\(837\) 15.1764i 0.524575i
\(838\) 6.38836 + 4.26857i 0.220682 + 0.147455i
\(839\) −41.3411 + 27.6232i −1.42725 + 0.953659i −0.428509 + 0.903538i \(0.640961\pi\)
−0.998743 + 0.0501217i \(0.984039\pi\)
\(840\) 1.99484 + 9.32956i 0.0688286 + 0.321901i
\(841\) 10.6875 4.42689i 0.368533 0.152652i
\(842\) 3.23028 7.79859i 0.111323 0.268757i
\(843\) −17.9998 + 12.0271i −0.619945 + 0.414234i
\(844\) 3.43470 + 5.14038i 0.118227 + 0.176939i
\(845\) 0.379115 2.05940i 0.0130420 0.0708456i
\(846\) −4.11829 + 4.11829i −0.141590 + 0.141590i
\(847\) 0.695657 + 3.49730i 0.0239031 + 0.120169i
\(848\) 7.58981 3.14380i 0.260635 0.107959i
\(849\) 49.4497 1.69711
\(850\) 1.83104 20.5341i 0.0628040 0.704312i
\(851\) −11.4944 −0.394022
\(852\) −37.0753 + 15.3571i −1.27018 + 0.526125i
\(853\) −0.190334 0.956873i −0.00651691 0.0327627i 0.977390 0.211444i \(-0.0678168\pi\)
−0.983907 + 0.178682i \(0.942817\pi\)
\(854\) 16.5164 16.5164i 0.565178 0.565178i
\(855\) −9.75944 + 53.0145i −0.333766 + 1.81306i
\(856\) −7.54818 11.2966i −0.257991 0.386111i
\(857\) −30.7890 + 20.5725i −1.05173 + 0.702744i −0.956209 0.292683i \(-0.905452\pi\)
−0.0955216 + 0.995427i \(0.530452\pi\)
\(858\) −12.8350 + 30.9865i −0.438180 + 1.05786i
\(859\) 14.2415 5.89904i 0.485915 0.201273i −0.126256 0.991998i \(-0.540296\pi\)
0.612172 + 0.790725i \(0.290296\pi\)
\(860\) −2.44887 11.4530i −0.0835057 0.390543i
\(861\) 40.2110 26.8681i 1.37039 0.915663i
\(862\) −7.22727 4.82911i −0.246162 0.164480i
\(863\) 2.05160i 0.0698374i −0.999390 0.0349187i \(-0.988883\pi\)
0.999390 0.0349187i \(-0.0111172\pi\)
\(864\) −1.55482 + 2.32695i −0.0528960 + 0.0791645i
\(865\) −7.13949 + 0.102086i −0.242750 + 0.00347103i
\(866\) 6.18312i 0.210111i
\(867\) −1.74744 + 45.1162i −0.0593462 + 1.53223i
\(868\) −6.16011 + 6.16011i −0.209088 + 0.209088i
\(869\) 54.3792 + 22.5246i 1.84469 + 0.764095i
\(870\) −14.0688 20.4174i −0.476978 0.692215i
\(871\) 0.973791 + 0.973791i 0.0329956 + 0.0329956i
\(872\) −5.28230 + 7.90551i −0.178881 + 0.267715i
\(873\) 7.99422 + 1.59015i 0.270563 + 0.0538184i
\(874\) 12.0680 + 2.40048i 0.408207 + 0.0811973i
\(875\) −0.770171 17.9444i −0.0260365 0.606632i
\(876\) 3.35963 + 8.11086i 0.113511 + 0.274041i
\(877\) 8.95406 + 13.4007i 0.302357 + 0.452509i 0.951273 0.308351i \(-0.0997772\pi\)
−0.648916 + 0.760860i \(0.724777\pi\)
\(878\) −3.29692 + 16.5747i −0.111266 + 0.559370i
\(879\) −10.2691 51.6265i −0.346370 1.74132i
\(880\) 7.46597 3.21832i 0.251678 0.108490i
\(881\) −30.3104 20.2528i −1.02118 0.682334i −0.0721137 0.997396i \(-0.522974\pi\)
−0.949071 + 0.315063i \(0.897974\pi\)
\(882\) 6.85555 + 16.5508i 0.230838 + 0.557293i
\(883\) −28.8886 28.8886i −0.972180 0.972180i 0.0274432 0.999623i \(-0.491263\pi\)
−0.999623 + 0.0274432i \(0.991263\pi\)
\(884\) −11.2438 + 8.86894i −0.378168 + 0.298295i
\(885\) 7.29625 + 16.9261i 0.245261 + 0.568964i
\(886\) −4.50217 + 10.8692i −0.151253 + 0.365158i
\(887\) −43.8005 + 8.71245i −1.47068 + 0.292535i −0.864434 0.502746i \(-0.832323\pi\)
−0.606241 + 0.795281i \(0.707323\pi\)
\(888\) 14.7545 0.495129
\(889\) −11.3563 + 2.25891i −0.380879 + 0.0757615i
\(890\) −9.21517 5.96859i −0.308893 0.200068i
\(891\) 3.35401 16.8617i 0.112363 0.564889i
\(892\) 10.1681 + 4.21177i 0.340454 + 0.141021i
\(893\) −7.89375 3.26970i −0.264154 0.109416i
\(894\) −9.51241 + 47.8221i −0.318143 + 1.59941i
\(895\) −3.61144 16.8902i −0.120717 0.564576i
\(896\) −1.57561 + 0.313408i −0.0526374 + 0.0104702i
\(897\) 19.0861 0.637266
\(898\) 0.743527 0.147897i 0.0248118 0.00493538i
\(899\) 8.66448 20.9179i 0.288976 0.697651i
\(900\) 13.9165 14.7360i 0.463883 0.491201i
\(901\) 32.5977 9.20330i 1.08599 0.306606i
\(902\) −29.1414 29.1414i −0.970301 0.970301i
\(903\) 8.55193 + 20.6462i 0.284590 + 0.687062i
\(904\) −16.5816 11.0794i −0.551495 0.368497i
\(905\) −14.4229 33.4588i −0.479434 1.11221i
\(906\) −0.212335 1.06748i −0.00705437 0.0354647i
\(907\) −5.14675 + 25.8744i −0.170895 + 0.859147i 0.796259 + 0.604956i \(0.206809\pi\)
−0.967154 + 0.254191i \(0.918191\pi\)
\(908\) −2.46236 3.68518i −0.0817163 0.122297i
\(909\) −14.6409 35.3462i −0.485607 1.17236i
\(910\) −8.69526 + 8.94753i −0.288245 + 0.296608i
\(911\) −6.98238 1.38888i −0.231337 0.0460157i 0.0780606 0.996949i \(-0.475127\pi\)
−0.309397 + 0.950933i \(0.600127\pi\)
\(912\) −15.4908 3.08132i −0.512953 0.102033i
\(913\) −12.7305 + 19.0525i −0.421317 + 0.630545i
\(914\) 21.3450 + 21.3450i 0.706030 + 0.706030i
\(915\) −84.9205 15.6330i −2.80738 0.516811i
\(916\) −0.0726235 0.0300817i −0.00239955 0.000993926i
\(917\) 7.54133 7.54133i 0.249037 0.249037i
\(918\) −7.49148 + 8.77635i −0.247256 + 0.289663i
\(919\) 32.8513i 1.08366i 0.840487 + 0.541832i \(0.182269\pi\)
−0.840487 + 0.541832i \(0.817731\pi\)
\(920\) −3.31789 3.22434i −0.109388 0.106303i
\(921\) −16.0764 + 24.0601i −0.529736 + 0.792806i
\(922\) 8.73931i 0.287814i
\(923\) −43.6358 29.1565i −1.43629 0.959699i
\(924\) −12.8985 + 8.61852i −0.424330 + 0.283529i
\(925\) −27.3871 4.63787i −0.900481 0.152492i
\(926\) 14.7652 6.11594i 0.485214 0.200982i
\(927\) 9.21977 22.2585i 0.302817 0.731065i
\(928\) 3.47152 2.31960i 0.113958 0.0761444i
\(929\) 2.87561 + 4.30365i 0.0943456 + 0.141198i 0.875640 0.482965i \(-0.160440\pi\)
−0.781294 + 0.624163i \(0.785440\pi\)
\(930\) 31.6728 + 5.83065i 1.03859 + 0.191195i
\(931\) −18.5833 + 18.5833i −0.609044 + 0.609044i
\(932\) −1.55811 7.83316i −0.0510376 0.256584i
\(933\) 26.8260 11.1117i 0.878242 0.363780i
\(934\) 41.6933 1.36425
\(935\) 32.1266 9.56830i 1.05065 0.312917i
\(936\) −14.0797 −0.460208
\(937\) 28.8813 11.9630i 0.943512 0.390816i 0.142724 0.989763i \(-0.454414\pi\)
0.800789 + 0.598947i \(0.204414\pi\)
\(938\) 0.124266 + 0.624729i 0.00405744 + 0.0203981i
\(939\) −10.8738 + 10.8738i −0.354854 + 0.354854i
\(940\) 1.82285 + 2.64542i 0.0594549 + 0.0862840i
\(941\) 17.1026 + 25.5958i 0.557528 + 0.834399i 0.997990 0.0633721i \(-0.0201855\pi\)
−0.440462 + 0.897771i \(0.645185\pi\)
\(942\) 34.8761 23.3035i 1.13632 0.759268i
\(943\) −8.97480 + 21.6671i −0.292260 + 0.705577i
\(944\) −2.86738 + 1.18771i −0.0933254 + 0.0386567i
\(945\) −5.46512 + 8.43785i −0.177780 + 0.274483i
\(946\) 15.8342 10.5801i 0.514815 0.343989i
\(947\) −38.8629 25.9674i −1.26287 0.843826i −0.269985 0.962864i \(-0.587019\pi\)
−0.992890 + 0.119038i \(0.962019\pi\)
\(948\) 42.9949i 1.39641i
\(949\) −6.37850 + 9.54609i −0.207055 + 0.309879i
\(950\) 27.7853 + 10.5888i 0.901473 + 0.343547i
\(951\) 0.304048i 0.00985942i
\(952\) −6.60311 + 0.521527i −0.214008 + 0.0169028i
\(953\) −37.4769 + 37.4769i −1.21400 + 1.21400i −0.244295 + 0.969701i \(0.578556\pi\)
−0.969701 + 0.244295i \(0.921444\pi\)
\(954\) 30.7671 + 12.7441i 0.996121 + 0.412607i
\(955\) 4.09273 2.82014i 0.132438 0.0912576i
\(956\) 0.509834 + 0.509834i 0.0164892 + 0.0164892i
\(957\) 22.3992 33.5227i 0.724062 1.08364i
\(958\) 39.7646 + 7.90968i 1.28474 + 0.255550i
\(959\) −11.8730 2.36168i −0.383398 0.0762626i
\(960\) 4.25894 + 4.13886i 0.137457 + 0.133581i
\(961\) −0.609403 1.47123i −0.0196582 0.0474590i
\(962\) 10.7199 + 16.0435i 0.345624 + 0.517263i
\(963\) 10.7447 54.0172i 0.346243 1.74068i
\(964\) 2.40690 + 12.1003i 0.0775210 + 0.389725i
\(965\) −5.66399 + 14.2469i −0.182330 + 0.458624i
\(966\) 7.34008 + 4.90448i 0.236163 + 0.157799i
\(967\) 5.25597 + 12.6890i 0.169021 + 0.408052i 0.985580 0.169209i \(-0.0541214\pi\)
−0.816560 + 0.577261i \(0.804121\pi\)
\(968\) 1.56953 + 1.56953i 0.0504467 + 0.0504467i
\(969\) −61.9400 20.1064i −1.98980 0.645912i
\(970\) 1.66100 4.17799i 0.0533315 0.134147i
\(971\) 6.59643 15.9252i 0.211690 0.511064i −0.781993 0.623287i \(-0.785797\pi\)
0.993683 + 0.112223i \(0.0357970\pi\)
\(972\) 20.5514 4.08792i 0.659186 0.131120i
\(973\) 30.2523 0.969845
\(974\) 16.0683 3.19619i 0.514862 0.102412i
\(975\) 45.4755 + 7.70106i 1.45638 + 0.246631i
\(976\) 2.83655 14.2603i 0.0907958 0.456461i
\(977\) 19.6258 + 8.12926i 0.627884 + 0.260078i 0.673854 0.738865i \(-0.264638\pi\)
−0.0459699 + 0.998943i \(0.514638\pi\)
\(978\) −21.1425 8.75750i −0.676062 0.280034i
\(979\) 3.48283 17.5094i 0.111312 0.559602i
\(980\) 9.66328 2.06620i 0.308682 0.0660022i
\(981\) −37.8018 + 7.51925i −1.20692 + 0.240071i
\(982\) −37.7944 −1.20607
\(983\) 24.1381 4.80136i 0.769885 0.153140i 0.205507 0.978656i \(-0.434116\pi\)
0.564379 + 0.825516i \(0.309116\pi\)
\(984\) 11.5203 27.8125i 0.367254 0.886629i
\(985\) −24.0155 + 10.3523i −0.765199 + 0.329851i
\(986\) 15.3362 7.81955i 0.488403 0.249025i
\(987\) −4.33456 4.33456i −0.137971 0.137971i
\(988\) −7.90439 19.0829i −0.251472 0.607107i
\(989\) −9.01068 6.02074i −0.286523 0.191448i
\(990\) 30.6257 + 12.1756i 0.973348 + 0.386965i
\(991\) 3.08725 + 15.5207i 0.0980698 + 0.493030i 0.998335 + 0.0576875i \(0.0183727\pi\)
−0.900265 + 0.435342i \(0.856627\pi\)
\(992\) −1.05795 + 5.31867i −0.0335899 + 0.168868i
\(993\) 41.9085 + 62.7204i 1.32992 + 1.99037i
\(994\) −9.28910 22.4259i −0.294632 0.711305i
\(995\) 31.4714 0.450003i 0.997710 0.0142660i
\(996\) −16.4164 3.26543i −0.520174 0.103469i
\(997\) 44.2479 + 8.80146i 1.40135 + 0.278745i 0.837185 0.546920i \(-0.184200\pi\)
0.564161 + 0.825665i \(0.309200\pi\)
\(998\) 16.2502 24.3202i 0.514392 0.769842i
\(999\) 10.9936 + 10.9936i 0.347823 + 0.347823i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 170.2.o.a.7.1 32
5.2 odd 4 850.2.v.c.143.1 32
5.3 odd 4 170.2.r.a.143.4 yes 32
5.4 even 2 850.2.s.c.7.4 32
17.5 odd 16 170.2.r.a.107.4 yes 32
85.22 even 16 850.2.s.c.243.4 32
85.39 odd 16 850.2.v.c.107.1 32
85.73 even 16 inner 170.2.o.a.73.1 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.o.a.7.1 32 1.1 even 1 trivial
170.2.o.a.73.1 yes 32 85.73 even 16 inner
170.2.r.a.107.4 yes 32 17.5 odd 16
170.2.r.a.143.4 yes 32 5.3 odd 4
850.2.s.c.7.4 32 5.4 even 2
850.2.s.c.243.4 32 85.22 even 16
850.2.v.c.107.1 32 85.39 odd 16
850.2.v.c.143.1 32 5.2 odd 4